Question $5$

Language $L_5$ is the language with adding conditional branches $"$if$0e_1$ then $e_2$ else $e_3"$

to $L_4,$ i$.$e$.,$ the syntax of $L_5$ is given as follows:

$e(exp.)$ ::$=n|e|e_{1}o+e_2|$ ifo $e_1$ then $e_2$ else $e_3$

Conditional branch $"$if $e_1$ then $e_2$ else $e_3"$ evaluates to $e_2$ if $e_1$ evaluates to $0$ and

evaluates to $e_3$ otherwise. For example,

ifo $(ifo0$ then $1$ else $2)$ then $3$ else $4$ ifo $1$ then $3$ else $44.$

Define the small$-$step operational semantics $($rules$)$ of conditional branches.